Spherical Potential Research Articles

Scattering of N2O on electron impact over an extensive energy range (0.1 eV–2000 eV)

We report electron impact total cross sections, Q(T), for e-N(2)O scattering over an extensive range of impact energies approximately from 0.1 eV to 2000 eV. We employ an ab initio calculation using R-matrix formalism below the ionization threshold of the target and above it we use the well established spherical complex optical potential to compute the cross sections. Total cross section is obtained as a sum of total elastic and total electronic excitation cross sections below the ionization threshold and above the ionization threshold as a sum of total elastic and total inelastic cross sections. Ample cross section data for e-N(2)O scattering are available at low impact energies and hence meaningful comparisons are made. Good agreement is observed with the available theoretical as well as experimental results over the entire energy range studied here.

Total (complete) and ionization cross-sections of argon and krypton by positron impact from 15 to 2000 eV – Theoretical investigations

Considering interactions and scattering of positrons with argon (Ar) and krypton (Kr) atoms, we have calculated total cross-sections (Q T = Q el + Q inel ) using complex spherical potentials for these systems. In positron–atom scattering it is difficult to bifurcate the ionization and cumulative excitation contained in the total inelastic cross-section. An approximate method called CSP-ic (complex scattering potential-ionization contribution) similar to electron–atom scattering has been applied to bifurcate ionization and cumulative excitation cross-sections at energies from the threshold to 2000 eV. Adequate comparisons of the present results are made, with available data.

Distance estimates in the Milky Way using tidal streams

AbstractDuring the past 20 years, numerous stellar streams have been discovered in both the Milky Way and the Local Group. These streams have been tidally torn from orbiting systems, which suggests that most should roughly trace the orbit of their progenitors around the Galaxy. As a consequence, they play a fundamental role in understanding the formation and evolution of our Galaxy. This project is based on the possibility of applying a technique developed by Binney to various tidal streams and overdensities in the Galaxy. The aim is to develop an efficient method to constrain the Galactic gravitational potential, to determine its mass distribution, and to test distance measurements. Here we apply the technique to the Grillmair & Dionatos GD-1 cold stellar stream. In the unrealistic case of noise-free data, the results show that the technique provides excellent discrimination against incorrect potentials and that it is possible to predict the heliocentric distance very accurately. This changes dramatically when errors are taken into account, which wash out most of the results. Nevertheless, it is still possible to rule out spherical potentials and set constraints on the distance of a given stream.

Phenomenological formula for alpha-decay half-lives

A phenomenological formula is presented for the partial half-life from the Q value for α decay. It is constructed in a conventional way by considering the penetrability of a charged particle in a spherical Coulomb potential. Parameters in the formula are fixed because they are determined by physical constants except for the following three adjustable parameters: the product of the collision frequency of an α particle and the formation probability, N; the distance between the charge radius and the radius of an inner point of the Coulomb barrier, r 0; and the odd-mass hindrance, h 0. The values obtained for the three adjustable parameters are reasonable, in contrast with those of conventional models such as the Viola–Seaborg formula. The root-mean-square deviations from experimental partial half-lives for even–even, odd-A, and odd–odd nuclei are 0.344, 0.740, and 0.940 (in log10), respectively. The obtained formula gives half-lives that are two or three times longer than those obtained using the Viola–Seaborg formula in the superheavy nuclear mass region.

A meta-cognitive sequential learning algorithm for neuro-fuzzy inference system

In this paper, we present a meta-cognitive sequential learning algorithm for a neuro-fuzzy inference system, referred to as, ‘Meta-Cognitive Neuro-Fuzzy Inference System’ (McFIS). McFIS has two components, viz., a cognitive component and a meta-cognitive component. The cognitive component employed is a Takagi–Sugeno–Kang type-0 neuro-fuzzy inference system. A self-regulatory learning mechanism that controls the learning process of the cognitive component, by deciding what-to-learn, when-to-learn and how-to-learn from sequential training data, forms the meta-cognitive component. McFIS realizes the above decision by employing sample deletion, sample reserve and sample learning strategy, respectively. The meta-cognitive component use the instantaneous error of the sample and spherical potential of the rule antecedents to select the best training strategy for the current sample. Also, in sample learning strategy, when a new rule is added the rule consequent is assigned such that the localization property of Gaussian rule is fully exploited. The performance of McFIS is evaluated on four regression and eight classification problems. The performance comparison shows the superior generalization performance of McFIS compared to existing algorithms.

Photoionization of atoms encapsulated by cages using the power-exponential potential

The systems of confined atoms in cages have received considerable attention for decades due to interesting phenomena arising from the effect of cage environment on the atom. For early theoretical work based on empirical model potentials, the Dirac δ-potential, i.e. the so-called bubble potential, and the attractive short-range spherical shell potential are conventionally used for the description of interaction between the valence electron of confined atom and the cage. In this work, the power-exponential potential with a flexible confining shape is proposed to model the cages. The methods of complex scaling in the finite-element discrete variable representation are implemented to investigate the hydrogen, hydrogen-like ions and alkali metals encapsulated by the cages. The energy spectrum varying with the confining well depth exhibits avoided crossings. The influence of cage on atomic photoionization leading to the oscillation behaviour or the so-called confinement resonances in cross sections is demonstrated in a variety of confined atomic systems. In comparisons with existing predictions using the Dirac δ-potential and the attractive short-range spherical shell potentials, our results show the significant influence of cage thickness and smooth shell boundary on the photoionization. The drastic changes of cross sections due to the character of cage are presented and discussed for the encaged lithium and sodium atoms. The present model is useful for clarifying the boundary effect of confining shell on the endohedral atoms.

Broken degeneracies: the rotation curve and velocity anisotropy of the Milky Way halo

Abstract We use distant blue horizontal branch stars with Galactocentric distances 16 < r < 48 kpc as kinematic tracers of the Milky Way dark halo. We model the tracer density as an oblate, power law embedded within a spherical power-law potential. Using a distribution function method, we estimate the overall power-law potential and the velocity anisotropy of the halo tracers. We measure the slope of the potential to be γ∼ 0.4, and the overall mass within 50 kpc is ∼4 × 1011 M⊙. The tracer velocity anisotropy is radially biased with β∼ 0.5, which is in good agreement with local solar neighbourhood studies. Our results provide an accurate outer circular velocity profile for the Milky Way and suggest a relatively high-concentration dark matter halo (cvir∼ 20).

Global earth isostatic model using smoothed Airy-Heiskanen and Vening Meinesz hypotheses

Isostatic hypotheses are used for different purposes in geophysics and geodesy. The Erath crustal thickness modelling is more complicated than the classical isostatic models. In this study we try to modify Airy-Hesiskanen model, utilizing a smoothing factor, to a model with regional or global isostatic model through a modern solution of the gravimetric-isostatic Vening Meinesz model and CRUST.0. In Airy-Hesiskanen's theory there is no correlation between neighbouring crustal columns, while this must be the case in reality due to the elasticity of the Earth. The idea is to keep the simplicity of the Airy-Heiskanen model, because it needs only the topographic data, and change the model which becomes to a model with regional/global isostatic model. The isostatic assumption for compensating the topographic potential is incomplete, as there are other geophysical phenomena which should be considered. Using the isostatic hypothesis for determining the depth of crust causes some disturbing signals in the gravity anomaly (approximately 285 mGal), which influence the crustal thickness determination. In this paper a simple method use for removing these effects. Spherical harmonic potential coefficients of the topographic compensation masses are used for modifying Airy-Heiskanen's model in a least-square adjustment procedure by estimating smoothing factor. The numerical analysis shows that below degree 10, the modified Airy-Hesiskanen and Vening Meinesz models are close together. Smoothing factors for modifying the Airy-Hesiskanen model vary from 0.75 to 0.64 between degrees 200 and 2159.

Electron ionization of NF3

Experimental and theoretical study on electron ionization of NF3 is carried out in terms of the absolute partial and total ionization cross sections. The measurements are done in crossed electron beam-molecular beam geometry for electron incident energies ranging from 0 to 500eV using a newly built time of flight mass spectrometer with emphasis on complete collection, transmission and detection without mass and energy discrimination, while maintaining reasonable mass resolution. The cross sections are put on the absolute scale using the relative flow technique. The partial cross sections and the thresholds for the formation of NF3+, NF2+, NF+, F+, and N+ are compared with the previous results. Our cross section values for lower mass ions N+, F+, NF+ are found to be considerably higher as compared to previous measurements. We also have calculated the total scattering and total ionization cross sections using the spherical complex optical potential (SCOP) formalism and compared with existing data. While the total scattering calculations agree with the existing experimental results, the total ionization cross sections do not agree well with our experimental data. The present experimental results agree with those estimated using “Deutsch–Mark formulation with new additivity rules”, which were not in agreement with the existing experimental results for the case of NF3.

Calculating neutron single-particle energies for Zr isotopes near N = 50, 70, 82

The neutron single-particle energies for Zr isotopes with neutron number N near 50, 70, and 82 are calculated using a mean field model with spherical dispersive optical potential. The calculated energy values are in good agreement with experimental data and with predictions according to mass formula KTUY05.

External electric field, hydrostatic pressure and temperature effects on the binding energy of an off-center hydrogenic impurity confined in a spherical Gaussian quantum dot

Based on the effective-mass approximation within a matrix diagonalization scheme, simultaneous effects of external electric field, hydrostatic pressure and temperature on the binding energy of an off-center hydrogenic donor confined by a spherical Gaussian potential have been calculated. The binding energy dependencies on the dot radius, the potential depth, the impurity position, the electric field strength, the hydrostatic pressure and the temperature are reported. We found that, not only the internal parameters (such as: the dot radius, the potential depth and the impurity position) but also the external perturbations (such as: electric field strength, hydrostatic pressure and temperature) have a great influence on the impurity binding energy.

Computation of the total scattering cross sections for electron impact on HCl and HBr between 0.1 eV and 2000 eV

In this paper total cross sections (QT) for electron impact on HCl and HBr are reported over a wide energy range from circa 0.1 eV to 2 keV. At impact energies below the ionization energy, the R-Matrix method is employed using Quantemol-N software whilst above the ionization energy the spherical complex optical potential (SCOP) method is used. It is shown that the two methods provide complimentary cross sections where they overlap. These calculations are compared with experimental and theoretical results wherever available.

Absolute free energy of binding of avidin/biotin, revisited.

The binding of biotin to avidin is one of the strongest in nature with absolute free energy of binding, ΔA(0) = -20.4 kcal/mol. Therefore, this complex became a target for a large number of computational studies, which all, however, are based on approximate techniques or simplified models and have led to a wide range of results Therefore, ΔA(0) is calculated here by rigorous statistical mechanical methods and models that consider long-range electrostatics. (1) We apply our method, "hypothetical scanning molecular dynamics with thermodynamic integration" (HSMD-TI) to avidin-biotin modeled by periodic boundary conditions with particle mesh ewald (PME). (2) We apply the double decoupling method (DDM) to this system modeled by the spherical solvent boundary potential (SSBP) and the generalized solvent boundary potential (GSBP). The corresponding results for neutral biotin, ΔA(0) = -29.1 ± 0.8 and -25.2 ± 0.5 kcal/mol are significantly lower than the experimental value; we also provide the result for a charged biotin, ΔA(0) = -33.3 ± 0.8 kcal/mol. It is plausible to suggest that this disagreement with the experiment may stem from ignoring the (positive) contribution of a mobile loop that changes its structure upon ligand binding.

Phase equilibrium modeling of gas hydrate systems for CO2 capture

Two thermodynamic models capable of describing dissociation pressures of mixed gas clathrate hydrates formed from ternary mixtures of CO2, N2 and liquid water, are presented. Both of the models utilize the Cubic-Plus-Association (CPA) equation of state (EOS) for the thermodynamic description of the non-solid phases (vapor and liquid). The solid hydrate phase is described by the van der Waals–Platteeuw model as presented by Parrish and Prausnitz. An algorithm for combining the CPA EOS with the van der Waals–Platteeuw model in a calculation of hydrate dissociation pressure is presented.Two models are described in this work. They differ in their method for describing the Langmuir adsorption coefficients in the van der Waals–Platteeuw model. These models are named Model I and Model II. Model I utilizes a statistical thermodynamics approach based on Lennard-Jones–Devonshire theory, using the spherical core Kihara cell potential. Model II uses a two-parameter explicit expression for the Langmuir adsorption coefficient, based on Langmuir adsorption theory. With two hydrate formers, four parameters in the Kihara cell potentials are fitted for Model I. Sixteen parameters are required to be fitted for Model II. The two model parameter sets are fitted to pure hydrate dissociation pressures and mixed hydrate dissociation pressures found in literature. In the fitting process, vapor phases with initial mole fractions of CO2 below 0.15 are assumed to form structure II hydrates, while structure I hydrates are assumed to form from vapor phases with initial mole fractions of CO2 at or above 0.15.The two models are validated against mixed hydrate equilibrium data found in literature. Both dissociation pressures and hydrate compositions are considered in the validation process.With the fitted parameters, Model I predicts a hydrate structure transition from structure II hydrates at vapor phase mole fractions of CO2 below 0.12 to 0.16 (depending on temperature) to structure I hydrates at mole fractions of CO2 above this concentration range. The exact transition concentration is shown to increase with increasing temperature. Model II predicts structure I hydrates to be stable in concentrations down to vapor phase mole fractions of CO2 in the order of 0.001 to 0.02, depending on temperature. Model II predicts the transition concentration to decrease with increasing temperature.Since there is disparity amongst the different literature data for this system, it was not possible to determine unequivocally, which of the two models perform better.

Neutron cross-sections for ^{55}Mn in the energy range from 0.2 to 22 MeV

Neutron total and differential elastic scattering cross-sections for ^{55}Mn nucleus was calculated from different global spherical optical potential (SOP) sets for different neutron energies ranging from 0.2 MeV to 22 MeV using the well known computer program SCAT-2 on an IBM PC-AT. In addition, the angular distributions of elastically scattered neutrons at different neutron energies were calculated. The results were compared with those of the experimental data obtained from the EXFOR data file of NEA data bank. The best-fit potential parameter was thereby selected. It was observed that the best fit to the experimental values of the total cross-sections are obtained by SOP parameters of Kawai for ^{55}Mn. Furthermore, the variations of the total cross-sections as a function of real potential depth V_0 and real radius parameter r_0 were calculated to observe the sensitivity of these parameters towards the cross-sections.

Scaling properties of net information measures for bound states of spherical model potentials confined with finite barrier #

Using dimensional analyses, the scaling properties of the Heisenberg uncertainty relationship as well as the various information theoretical uncertainty-like relationships are derived for the bound states corresponding to the superposition of the power potential of the form \(V(r)=Zr^n+\sum_i Z_i r^{n_i}\), where Z, Z i , n, n i are parameters, in the free state as well as in the additional presence of a spherical penetrable boundary wall located at radius R The uncertainty product and all other net information measures are shown here to depend only on the parameters [s i ] defined by the ratios \(Z_i/Z^{(n_i+2)/(n+2)}\). Introduction of a finite potential, V c at the radial distance r ≥ R results in a complete set of scaling parameters given by [s i , t 1, t 2], where t 1 is given by RZ 1/(n + 2) and \(t_2= V_c /(Z)^{2/(n+2)}\). The scaling of the sum of Shannon information entropy, S T , with the nuclear charge, Z, for the hydrogen isoelectronic series confined inside an impenetrable cavity of radius R . The optimum value of S T remains fixed for all Z, while the location of R opt scales as 1/Z.

Systematic study of the rf-induced evaporation of 87Rb atoms in a spherical magnetic quadrupole trap

We trap 87Rb atoms in a spherical magnetic quadrupole potential consisting of a pair of anti-Helmholtz coils. The number of trapped atoms is 2.16(7)×108, and the lifetime is 26 seconds. The number, the temperature and the size of the atoms in a magnetic trap are controlled by the forced rfevaporative cooling technique. We obtain a sub-Doppler temperature of 33.7(5) μK in these atoms at an evaporation frequency of 4.2 MHz in the magnetic quadrupole trap. We discuss the properties of the atoms in the spherical magnetic quadrupole trap and the results of the rf-evaporation process.

Relaxation to quantum equilibrium for Dirac fermions in the de Broglie–Bohm pilot-wave theory

Numerical simulations indicate that the Born rule does not need to be postulated in the de Broglie–Bohm pilot-wave theory, but tends to arise dynamically (relaxation to quantum equilibrium). These simulations were done for a particle in a two-dimensional box whose wave function obeys the non-relativistic Schrödinger equation and is therefore scalar. The chaotic nature of the de Broglie–Bohm trajectories, thanks to the nodes of the wave function which yield to vortices, is crucial for a fast relaxation to quantum equilibrium. For spinors, we typically do not expect any node. However, in the case of the Dirac equation, the de Broglie–Bohm velocity field has vorticity even in the absence of nodes. This observation raises the question of the origin of relaxation to quantum equilibrium for fermions. In this article, we provide numerical evidence to show that Dirac particles also undergo relaxation, by simulating the evolution of various non-equilibrium distributions for two-dimensional systems (the two-dimensional Dirac oscillator and the Dirac particle in a two-dimensional spherical step potential).

Thermal instability in gravitationally stratified plasmas: implications for multiphase structure in clusters and galaxy haloes

We study the interplay among cooling, heating, conduction, and magnetic fields in gravitationally stratified plasmas using simplified, plane-parallel numerical simulations. Since the physical heating mechanism remains uncertain in massive halos such as groups or clusters, we adopt a simple, observationally-motivated prescription which enforces global thermal equilibrium when averaged over large scales. The plasma remains susceptible to local thermal instability, however, and cooling drives an inward flow of material. In contrast to previous results, we argue that the thermal stability of the plasma is independent of its convective stability. We find that the ratio of the cooling timescale to the dynamical timescale t_cool/t_ff controls the saturation of the thermal instability: when t_cool/t_ff < 1, the plasma develops extended multi-phase structure, whereas when t_cool / t_ff > 1 it does not. (In a companion paper, we show that the criterion for thermal instability in a spherical potential is somewhat less stringent, t_cool / t_ff < 10.) When thermal conduction is anisotropic with respect to the magnetic field, the criterion for multi-phase structure is essentially independent of the thermal conductivity of the plasma. Our criterion for local thermal instability to produce multi-phase structure is an extension of the cold vs. hot accretion modes in galaxy formation that applies at all radii in hot halos, not just to the virial shock. We show that this criterion is consistent with data on multi-phase gas in the ACCEPT sample of clusters; in addition, when t_cool / t_ff > 1, the net cooling rate to low temperatures and the mass flux to small radii are suppressed enough relative to models without heating to be qualitatively consistent with star formation rates and x-ray line emission in groups and clusters.

Calculations of total ionization cross sections for halogen compounds on electron impact from threshold to 2 keV

Calculation for electron impact total ionization cross sections on halogen compounds (BF, SiF, BCl, SiCl) are performed employing Spherical Complex Optical Potential and Complex Optical Potential — ionization contribution (CSP-ic) formalisms. In this article we are presenting data for energies ranging from above threshold to 2000 eV. Our results are compared with available experimental and theoretical data wherever available. It is found that the present result gives a better account of the ionization cross sections.